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TABLE 4.3
Transfer Matrix for a Beam Element, Part c:
λ>
0,
λ
−
ζη>
0
λ
=
0
,
λ
−
ζη
=
1
4
2
1
4
2
,
1
4
2
λ<
0
λ
−
ζη
=
(ζ
−
η)
λ
−
ζη<
(ζ
−
η)
ζ
−
η
=
0
λ
−
ζη>
(ζ
−
η)
0
1.
2.
4.
6.
8.
2
2
1
2
b
2
a
2
,p
A
=
cosh
a
,
B
=
cos
b
ζ>
0:
α
=
ζ
ζ
−
η>
0:
β
=
(ζ
−
η)
ζ
−
η>
0:
g
=
−
=
1
A
=
cosh
a
,
B
=
cos
b
C
=
sinh
a
,
D
=
sin
b
A
=
cos
a
A
=
cos
β
,
B
=
β
sin
β
A
=
cos
a
,
B
=
cos
b
C
=
sinh
a
,
D
=
sin
b
2
√
λ
−
ζη
−
a
2
b
2
g
=
+
B
=
(
sin
a
)/α
C
=
(
sin
β)/β
C
=
sin
a
,
D
=
sin
b
=
β
2
(ζ
−
η)
−
4
(ζ
+
η)
1
1
4
(ζ
−
η)
a
2
=
a
2
1
4
(ζ
+
η)
1
2
(ζ
−
η)
a
2
1
4
+
2
−
=
2
−
λ
2
√
λ
−
ζη
+
=
β
2
(ζ
−
η)
+
4
(ζ
+
η)
3.
5.
b
2
1
1
4
(ζ
−
η)
=
b
2
1
4
(ζ
+
η)
1
2
(ζ
−
η)
b
2
1
4
+
2
+
2
2
1
2
(ζ
−
η)
=
2
−
λ
ζ<
0:
α
=−
ζ
ζ
−
η<
0:
β
=−
4
β
=−
λ
A
=
cosh
α
A
=
cosh
β
,
B
=−
β
sinh
β
B
=
(
sinh
α)/α
C
=
(
sinh
β)/β
7.
ζ
−
η<
a
2
b
2
,
p
0:
g
=
−
=−
1
A
=
cosh
a
,
B
=
cosh
b
C
=
sinh
a
,
D
=
sinh
b
(ζ
−
η)
+
4
(ζ
+
η)
a
2
1
2
=−
2
−
λ
2
(ζ
−
η)
−
4
(ζ
+
η)
1
b
2
2
=−
−
λ
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